Detection and quantification of inverse spin Hall effect from spin pumping in permalloy/normal metal bilayers

The precession of the magnetization of a ferromagnet is shown to transfer spins into adjacent normal metal layers. This "pumping" of spins slows down the precession corresponding to an enhanced Gilbert damping constant in the Landau-Lifshitz equation. The damping is expressed in terms of the scattering matrix of the ferromagnetic layer, which is accessible to model and first-principles calculations. Our estimates for permalloy thin films explain the trends observed in recent experiments.

Hirsch [Phys. Rev. Lett. 83, 1834 (1999)] recently proposed a spin Hall effect based on the anomalous scattering mechanism in the absence of spin-flip scattering. Since the anomalous scattering causes both anomalous currents and a finite spin-diffusion length, we derive the spin Hall effect in the presence of spin diffusion from a semiclassical Boltzmann equation. When the formulation is applied to certain metals and semiconductors, the magnitude of the spin Hall voltage due to the spin accumulation is found to be much larger than that of magnetic multilayers. An experiment is proposed to measure this spin Hall effect.